Kitchen sinks in properties built before the eighties generally go out to an outside drain and the problem is normally rust in the outlet pipe and fats or roots in the outside drain or gulley. This is usually quite a simple task to clean and can be cleared with an electric drain cleaning machine.
Properties built after the eighties generally have the kitchen sink a long way from the main drains. The kitchen sink drain usually is a smaller pipe than the main drain and runs a long distance underneath the concrete slab of the house and connects directly into the main drain.
The blockage is normally just fat build up over time plus the design factor which is prone to blockages .The only way to clear this type of blockage with out any dismantling or lifting pavers is from the kitchen sink itself. Specialised drain cleaning machines or high pressure water jetters need to be utilised.